Weak pseudocompactness on spaces of continuous functions
type: Item
instance of: scholarly article
title: Weak pseudocompactness on spaces of continuous functions
zbMATH Open document ID: 1329.54020
author: R. Rojas-Hernández
author: Alejandro Dorantes-Aldama
author: Angel Tamariz-Mascarúa
published in: Topology and its Applications
publication date: 2015-11-16T00:00:00Z
review text: The authors analyze, in a purely theoretical setting that lies in the framework of General Topology, a variant of compactness named weak pseudocompactness. Namely, a topological space \(X\) is said to be weakly pseudocompact if it is \(G_\delta\)-dense in at least one of its compactifications. This study is also related to the analysis of continuous extensions of maps between abstract topological spaces. Thus, a space \(X\) satisfies the property \(D_Y\) if for every countable discrete and closed subset \(N\) of \(X\), every function \(f:N \rightarrow Y\) can be continuously extended to a function over all of \(X\) (and with codomain \(Y\)). In the present paper the authors analyze weak pseudocompactness of spaces of continuous functions from a topological space \(X\) into another space \(Y\). Throughout this study the authors relate the results obtained in this setting to the analysis of several completeness properties defined by topological games such as the Banach--Mazur game as well as the Choquet game.
reviewed by: Esteban Induraín
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54C45
Mathematics Subject Classification ID: 91A44
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D45
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 6509435
zbMATH Keywords: weakly pseudocompact space
zbMATH Keywords: space of continuous functions
zbMATH Keywords: pseudo-complete space
zbMATH Keywords: weakly \(\alpha\)-favorable space
zbMATH Keywords: \(\omega\)-discrete space
zbMATH Keywords: \(C_\omega\)-discrete space
zbMATH Keywords: \(b\)-discrete space
zbMATH Keywords: Banach-Mazur game
zbMATH Keywords: Choquet game
zbMATH Keywords: Lutzer-McCoy game
MaRDI profile type: Publication
full work available at URL: j.topol.2015.09.010
OpenAlex ID: W2100023034
cites work: Pseudo-completeness and the product of Baire spaces
cites work: Topological groups and related structures
cites work: Q5571890
cites work: On some generalizations of compactness in spaces \(C_p(X,2)\) and \(C_p(X,\mathbb Z)\)
cites work: The partially pre-ordered set of compactifications of \(C_p(X,Y)\)
cites work: Q5186348
cites work: Sums, products, and mappings of weakly pseudocompact spaces
cites work: Q4297859
cites work: Q4092470
cites work: Stationary strategies in topological games
cites work: Rings of Real-Valued Continuous Functions. I
cites work: Category in function spaces. I
cites work: Topological properties of spaces of continuous functions
cites work: Pseudocomplete and weakly pseudocompact spaces
cites work: Q4457272
cites work: Cartesian products of Baire spaces
cites work: Baire property of spaces of continuous functions
cites work: Q4708166
cites work: A pseudocompact Tychonoff space all countable subsets of which are closed and \(C^*\)-embedded
cites work: Q3417821
cites work: Remarks on a game of Choquet
cites work: The spaces \(C_ p(X):\) decomposition into a countable union of bounded subspaces and completeness properties
cites work: Quasiregular, pseudocomplete, and Baire spaces
cites work: Topological Spaces That are α-Favorable for a Player with Perfect Information
DOI: 10.1016/J.TOPOL.2015.09.010
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description: scientific article; zbMATH DE number 6509435